Theorem G.2 (Theorem III.7(2) in [1]}) 

Let \(\phi : \operatorname{Gr}(n,r) \rightarrow \operatorname{Gr}(n,r)\)  be a local diffeomorphism.
Let \(\mathbf {P}\in \operatorname{Gr}(n,r)\)  be a fixed point of \(\phi \) . There exist an open neighborhood \(B_\mathbf {P}\subseteq \operatorname{Gr}(n,r)\)  of \(\mathbf {P}\)  and a smoothly embedded disk \(W_\mathbf {P}\subseteq \operatorname{Gr}(n,r)\)  containing \(\mathbf {P}\)  such that
